we have the expression
x^2+9x+20
Complete the square
equate the expression to zero
x^2+9x+20=0
group terms
(x^2+9x)=-20
x^2+9x+(9/2)^2-(9/2)^2=20
x^2+9x+(9/2)^2=20+(9/2)^2
Rewrite as perfect squares
(x+9/2)^2=-20+81/4
(x+9/2)^2=1/4
take square root on both sides
[tex](x+\frac{9}{2})=\pm\sqrt[]{\frac{1}{4}}[/tex]simplify
[tex]\begin{gathered} x+\frac{9}{2}=\pm\frac{1}{2} \\ x=-\frac{9}{2}\pm\frac{1}{2} \end{gathered}[/tex]the values of x are
x=-4 and x=-5
therefore
the given expression in factored form is
x^2+9x+20=(x+4)(x+5)
another way to find out the factored form
the formula to solve a quadratic equation of the form
ax^2+bx+c=0
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this problem we have
x^2+9x+20=0
so
a=1
b=9
c=20
substitute in the formula
[tex]x=\frac{-9\pm\sqrt[]{9^2-4(1)(20)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{-9\pm\sqrt[]{1}}{2} \\ x=\frac{-9\pm1}{2} \\ x=\frac{-9+1}{2}=-4 \\ x=\frac{-9-1}{2}=-5 \end{gathered}[/tex]the values of x are
x=-4 and x=-5
therefore
the factored form is
(x+4)(x+5)